Review_poblems_MTH205_Exam2_F07

Review_poblems_MTH205_Exam2_F07 - MTH205 Practice Problems...

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MTH205: Practice Problems Exam 2 / Fall 07 Q1. Find an interval around 0 = x for which the initial value problem ) sin( ' 4 1 ' ' ) 1 ( 2 x y y x y x = + - + - , 1 ) 0 ( = y , 0 ) 0 ( ' = y has a unique solution. Q2. Consider the differential equation x e y y 2 4 = - a) Find the general solution c y of the corresponding homogeneous equation. b) Find a particular solution p y by the method of undetermined coefficients. c) Find the general solution. d) Determine the solution subject to the initial conditions: 2 ) 0 ( = y , 1 ) 0 ( = y Q3. Solve the same problem in Q.2 by the method of variation of parameters. Q4. Find the general solution of 3 2 6 4 x y y x y x = + - Q5. Given that x e y = 1 is a solution of the d.e. 0 ) 2 ( ) 1 ( = + + - + y y x y x , find the general solution. Q6. Given that 1 1 = y is a solution of the d.e. 0 = + y y , use the reduction of order method to find the general solution of 1 = + y y . Q7. Set up the appropriate form of the particular solution

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Review_poblems_MTH205_Exam2_F07 - MTH205 Practice Problems...

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